performance analysis and optimized design of backward-curved

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VOLUME 15, NUMBER 3 HVAC&R RESEARCH MAY 2009 461 Performance Analysis and Optimized Design of Backward-Curved Airfoil Centrifugal Blowers Chen-Kang Huang, PhD Mu-En Hsieh Received October 21, 2008; February 15, 2009 In this study, backward-curved airfoil centrifugal blowers were numerically simulated and com- pared with experimentally measured data. Simulation settings and boundary conditions are stated, and the measurements follow ANSI/AMCA Standard 210-07/ANSI/ASHRAE Standard 51-07, Laboratory Methods of Testing Fans for Certified Aerodynamic Performance Rating (AMCA/ASHRAE 2007). Comparing simulation results with measured data, it was found that the deviation of the static pressure curve at each specified flow rate was within 4.8% and the deviation of the efficiency curve was within 15.1%. After the simulation scheme was proven valid, the effects of blade angle, blade number, tongue length, and scroll contour were dis- cussed. Several parameter changes are suggested based on these simulations. An optimized design is presented with a 7.9% improvement in static pressure and a 1.5% improvement in effi- ciency. Overall, the whole process simulates backward-curved airfoil centrifugal blowers effec- tively and is a powerful design tool for blower development and improvement. INTRODUCTION A blower is a gap pump that is capable of providing moderate to high pressure rise and flow rate. Blowers are utilized widely in all kinds of engineering applications, such as building venti- lation, air-supply in processes, and consumer electronics. There are three main types of blowers used for moving air: axial, centrifugal, and mixed flow. Among the three main types, centrifu- gal blowers (shown in Figure 1) are commonly applied to general heating, ventilating, and air-conditioning applications. They are usually only applied to larger systems, which may be low-, medium-, or high-pressure applications, and large, clean-air industrial operations for sig- nificant energy saving. Depending on the blade design, centrifugal blowers can be categorized into forward-curved, backward-curved, radial, and airfoil types. While the first three types are relatively easy to manufacture, centrifugal blowers with airfoil type blades exhibit the following characteristics (ASHRAE 1996; Cengel and Cimbala 2006): highest efficiency of all centrifugal blower designs blade of airfoil contour curved away from direction of rotation air leaves impeller at velocity less than tip speed scroll-type design for efficient conversion of dynamic pressure to static pressure maximum efficiency requires close clearance and alignment between wheel and inlet highest efficiencies occur at 50% to 60% of wide open volume; the pressure characteristics around the peak efficiency point are still efficient power reaches maximum near peak efficiency and becomes lower, or self-limiting, toward free delivery Chen-Kang Huang is an assistant professor in the Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, Taipei, Taiwan. Mu-En Hsieh is a graduate student in the Institute of Mechatronic Engineering, Na- tional Taipei University of Technology, Taipei, Taiwan. ©2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC&R Research, Vol 15, No. 3, May/2009. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAE’s prior written permission.

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Page 1: Performance Analysis and Optimized Design of Backward-Curved

VOLUME 15, NUMBER 3 HVAC&R RESEARCH MAY 2009

©2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC&R Research, Vol 15, No. 3, May/2009.For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAE’s prior written permission.

Performance Analysis and Optimized Design of Backward-Curved Airfoil Centrifugal Blowers

Chen-Kang Huang, PhD Mu-En Hsieh

Received October 21, 2008; February 15, 2009

In this study, backward-curved airfoil centrifugal blowers were numerically simulated and com-pared with experimentally measured data. Simulation settings and boundary conditions arestated, and the measurements follow ANSI/AMCA Standard 210-07/ANSI/ASHRAE Standard51-07, Laboratory Methods of Testing Fans for Certified Aerodynamic Performance Rating(AMCA/ASHRAE 2007). Comparing simulation results with measured data, it was found thatthe deviation of the static pressure curve at each specified flow rate was within 4.8% and thedeviation of the efficiency curve was within 15.1%. After the simulation scheme was provenvalid, the effects of blade angle, blade number, tongue length, and scroll contour were dis-cussed. Several parameter changes are suggested based on these simulations. An optimizeddesign is presented with a 7.9% improvement in static pressure and a 1.5% improvement in effi-ciency. Overall, the whole process simulates backward-curved airfoil centrifugal blowers effec-tively and is a powerful design tool for blower development and improvement.

INTRODUCTIONA blower is a gap pump that is capable of providing moderate to high pressure rise and flow

rate. Blowers are utilized widely in all kinds of engineering applications, such as building venti-lation, air-supply in processes, and consumer electronics. There are three main types of blowersused for moving air: axial, centrifugal, and mixed flow. Among the three main types, centrifu-gal blowers (shown in Figure 1) are commonly applied to general heating, ventilating, andair-conditioning applications. They are usually only applied to larger systems, which may below-, medium-, or high-pressure applications, and large, clean-air industrial operations for sig-nificant energy saving. Depending on the blade design, centrifugal blowers can be categorizedinto forward-curved, backward-curved, radial, and airfoil types. While the first three types arerelatively easy to manufacture, centrifugal blowers with airfoil type blades exhibit the followingcharacteristics (ASHRAE 1996; Cengel and Cimbala 2006):

• highest efficiency of all centrifugal blower designs• blade of airfoil contour curved away from direction of rotation• air leaves impeller at velocity less than tip speed• scroll-type design for efficient conversion of dynamic pressure to static pressure• maximum efficiency requires close clearance and alignment between wheel and inlet• highest efficiencies occur at 50% to 60% of wide open volume; the pressure characteristics

around the peak efficiency point are still efficient• power reaches maximum near peak efficiency and becomes lower, or self-limiting, toward

free delivery

Chen-Kang Huang is an assistant professor in the Department of Bio-Industrial Mechatronics Engineering, NationalTaiwan University, Taipei, Taiwan. Mu-En Hsieh is a graduate student in the Institute of Mechatronic Engineering, Na-tional Taipei University of Technology, Taipei, Taiwan.

461

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Including the centrifugal blowers we focus on in this study, blowers can be analyzed theoreti-cally, then some basic performance characteristics can be derived and calculated from simpleequations (Logan 1993; Fox and McDonald 1998). The horsepower, which is the useful poweractually delivered to the fluid, can be written as Equation 1:

(1)

where ρ is the fluid density, g is the gravitational acceleration constant, Q is the volume flowrate, and H is the net head of the blower. The external power supplied to the pump is the brakehorsepower (bhp). Equation 2 provides the definition of brake horsepower:

(2)

where ω is the rotational speed of the shaft and Tshaft is the torque supplied to the shaft. Theblower efficiency, usually abbreviated as ηpump, then can be defined as follows:

(3)

The idealized velocity tangential and normal components are shown in Figure 2. The fluid isassumed to enter the impeller wheel at radius r1 with uniform absolute velocity V1 and to leavethe impeller wheel at radius r2 with uniform absolute velocity V2. The rate of work done on animpeller wheel can be written as

, (4)

where U is the tangential speed of the impeller wheel at radius r and is the mass flow rate.The head added to the flow, which is the dimension of length, can be written as

. (5)

Figure 1. Explosion view of a typical centrifugal blower.

W· horsepower ρ g Q H⋅⋅⋅=

bhp W· shaft ω Tshaft⋅= =

ηpumpW· horsepower

bhp------------------------------ ρ g Q H⋅⋅⋅

ω Tshaft⋅----------------------------= =

bhp ω Tshaft⋅ ω r2 Vt2r1 Vt1

⋅–⋅( )⋅ m·⋅ U2 Vt2U1 Vt1

⋅–⋅( ) m·⋅= = =

H bhpm· g⋅----------- 1

g--- U2 Vt2

U1 Vt1⋅–⋅( )= =

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VOLUME 15, NUMBER 3, MAY 2009 463

If the fluid enters the impeller with purely radial absolute velocity, .The increase in head becomes

. (6)

Observing the exit velocity triangle in Figure 2, it can be found that

. (7)

Then

, (8)

where represents the ideal flow rate for an impeller of width w. The theoret-ical derivations in Equations 1–8 estimate the performance of ideal blowers. But, these equa-tions cannot investigate several effects on actual blower performance, such as number of bladesand scroll contour. More powerful tools are necessary to take more design parameters intoaccount to better estimate the blower performance and facilitate the design process.

Computational fluid dynamics (CFD) packages have progressed to the point where they canproduce accurate predictions for thermal and fluid applications (Gonzalez et al. 2002; Kim andSeo 2004; Medvitz et al. 2002; Tsai and Wu 2007; Velarde-Suarez et al. 2001). Subhash andMajumder (2007) used FLUENT (Fluent 2005a) to solve a large eddy simulation (LES) modelfor the film cooling problem. After the time-dependent analysis, they obtained the temperature,pressure, and velocity distributions. Numerous researchers have used CFD simulations to studyturbo-machinery. Calvert and Ginder (1999) studied transonic fans and compressors. In their

Figure 2. Velocity vector diagram of impeller wheel in a backward-curved blower.

vt10=

HU2 Vt2

g------------------=

Vt2U2 Vn2cot β2( )–=

HU2

2 U2– Vn2cot β2( )⋅g

----------------------------------------------------U2

2

g-------

U2 cot β2( )⋅2π r2 w g⋅ ⋅ ⋅--------------------------------Q–= =

Q 2π r2 w Vn2⋅ ⋅ ⋅=

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study, the evolution of transonic compressor designs and methods was outlined, followed bymore detailed descriptions of current compressor configurations and requirements and modernaerodynamic design methods and philosophies. Detailed quasi-three-dimensional and three-dimensional computational fluid dynamics analyses were employed to refine the design. Lin andHuang (2002) numerically simulated the internal flow for a forward-curved centrifugal fan usedin notebook PC cooling. In their study, an integral solution, including design powered by CFD,prototype manufacturing, and experiment verification, was presented. With results from CFDsimulation, they concluded the optimum inlet angle design to smooth the airflow around theinlet. Thakur et al. (2002) used a CFD-based computational tool to analyze fluid flow in a cen-trifugal blower. Global quantities such as static pressure rise, horsepower, and static efficiencywere compared between calculation results and measured data. They concluded that the overallCFD predictions are satisfactory. Yu et al. (2005) carried out numerical simulation for a wholecentrifugal fan and derived the optimum design. A sample fan was manufactured and tested, andthe numerical prediction agrees well with the tested data. Katsumi and Tetsouo (1999) investi-gated the form of volute tongue that affects the characteristics of a centrifugal blower. They pre-sented visualized experiments and numerical calculations for the tongue shape of three types andclarified the flow characteristics of the flow near the tongue in a centrifugal blower. It was con-cluded that the behavior of the flow near the tongue agrees with that obtained by flow visualiza-tion experiments and that the stagnation point moves around the tongue when changing the massflow. Dilin et al. (1998) presented a detailed experimental study of the performance of tworadial-flow fan volutes. Their research included a volute with a full tongue and the same volutewith the tongue cut back to allow flow recirculation. A computational model, using the k–ε tur-bulence model, was used to predict the internal flow of both volutes. The performance of thevolutes was discussed, and the CFD analysis was used to recommend design improvements forthe volute.

NUMERICAL SIMULATIONIn this study, the commercial CFD package FLUENT is used to simulate four backward-

curved airfoil centrifugal blowers. The primary parameters of the four blowers are listed inTable 1. FLUENT solves the Navier-Stokes equation using the finite volume method (FVM),which has been applied widely in fluid mechanics and engineering applications. It has beenshown that the FLUENT quasi-steady simulation can be used to predict blower performance.The simulation results are compared with the measured results to verify the validity. This sec-tion states code verification, grid system generation, and boundary condition settings of thisstudy. For more details about the simulation scheme, please refer to the study by Hsieh (2007).

Model ConstructionFor this study, the three-dimensional blower models were first created in computer-aided

design (CAD) software (as shown in Figure 1) and exported into STEP files (ISO 2002). TheSTEP files were then imported into GAMBIT (Fluent 2005b), the mesh generator. In GAMBIT,model construction and split were processed. The fluid volume was split into a rotating fluidvolume, a scroll volume, an inlet cone volume, and an inlet/outlet duct volume. The inlet andoutlet ducts were intentionally set to simulate the actual measuring situation and to provide bet-ter boundary conditions for simulations. In this study, the length of the inlet duct was set to 10times the diameter of the inlet duct and the outlet duct length was set to 15 times the diameter ofthe outlet duct. Consequently, the flow was assumed fully developed when leaving the inlet andoutlet ducts. The impeller wheel volume was defined as a rotating reference frame with constantrotational speed, and other blocks were defined in a stationary frame. This setup is referred to asa “frozen rotor” model in other literature.

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Grid GenerationAccording to official GAMBIT technical documents (Fluent 2005b), the system automati-

cally chooses the most suitable elements for complex geometry. The rotating fluid and scrollvolumes were defined by tetrahedral/hybrid elements, and hex/wedge elements were selectedfor the inlet cone and inlet/outlet duct volumes. A typical grid system is shown in Figure 3. Gridindependency tests were performed for each model discussed in this study. To ensure the gridsystem was appropriate for high-speed flow, free delivery was selected to be the operating con-dition for the grid independency test. The inlet flow rate was then given as the inlet boundarycondition. The outlet boundary condition was set as static pressure equal to the atmosphericpressure. If the difference of the outlet flow rate caused by further increasing grid size wasbelow 1%, the grid size was taken to perform all simulations for the model. The records of gridindependency testing for Model A are shown in Figure 4. For each model, the same process andjudging philosophy were applied to choose the suitable grid size. The grid sizes for the fourmodels discussed in this study are listed in the row titled “Total grid size” in Table 1.

Table 1. Primary Parameters of Blowers Discussed in This Study*

Parameter Model A Model B Model C Model D

Impeller wheel outer diameter,a mm (in.)

910 (35 7/8)

829 (32 5/8)

752(29 5/8)

678(26 5/8)

Blade angle,b degrees 46.39

Blade number 12

Tongue length,c

mm (in.)214

(8 3/8)206

(8 1/8)190

(7 1/2)172

(6 3/4)

Impeller wheel width,d

mm (in.)224

(8 7/8)204(8)

181(7 1/8)

167(6 1/2)

Inlet diameter,e

mm (in.)924

(36 3/8)850

(33 1/2)765

(30 1/8)695

(27 3/8)

Outlet size,f

mm × mm (in. × in.)824 × 737

(32 1/2 × 29)670 × 760

(26 3/8 × 30)594 × 678

(23 3/8 × 265/8)544× 614

(21 3/8 × 241/8)

Total grid size 1,063,787 871,861 781,310 589,640

*Footnotes indicate the corresponding parameters in the schematic.

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Assumptions and Numerical ModelIn this study, several assumptions were made to facilitate the simulations:

1. incompressible flow2. no-slip boundary condition3. gravity effects are negligible4. fluid properties are not functions of temperature

Turbulence modeling is a key issue in most CFD simulations. Most engineering applicationsare turbulent and require a turbulence model to facilitate the calculation. In the past decades,algebraic models, one- and two-equation models, non-linear eddy viscosity models, algebraicstress models, Reynolds stress transport models, detached eddy simulations, LESs, and directnumerical simulations have been proposed to model the random nature. Among these models,

Figure 3. Grid system.

Figure 4. Grid independency tests for Model A: a) SI units, b) I-P units.

(a) (b)

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two-equation turbulence models are one of the most common turbulence models. Two-equationmodels include two extra transport equations to represent the turbulent properties of the flow.This allows a two-equation model to account for effects of convection and diffusion of turbulentenergy. One of the transported variables is the turbulent kinetic energy, k, which determines theenergy in the turbulence. The second transported variable is the turbulent dissipation, ε, whichcan be thought of as the variable that determines the length scale of the turbulence. The k-εmodel has become one of the industry standard models and is commonly used for most types ofengineering problems. In this study, the standard k-ε model with standard wall functions waschosen in the Viscous Model menu of the FLUENT solver. The SIMPLE numerical algorithmwas used (Fluent 2005a). In addition, the pressure parameter was discretized by second-ordercentral difference, and the parameters of k and ε were discretized by second-order upwindscheme.

Boundary Conditions

The boundary conditions for blowers discussed in this study consisted of inlet, outlet, andimpeller wheel boundary conditions. At the beginning of this study, the total pressure at theentrance of the inlet was given as the inlet boundary condition. It was found that this methodencountered some difficulties in converging in the low flow rate region of the performancecurve. The inlet flow rate was then given as the inlet boundary condition. The outlet boundarycondition was set as static pressure equal to the atmospheric pressure. Motion wall type wasselected to be the impeller wheel boundary condition, and the relative velocity between theimpeller wheel and the rotational volume was assumed to be zero.

Converging Criteria

While the convergence criteria were usually set at 10–5 for the residuals of all quantities, itwas observed that the residuals remained around 10–2 for high pressure/low flow rate condi-tions. For some other cases in this study, the numerical results could not converge to 10–5 butchanged periodically within a range around 10–3 to 10–4. This has also been observed by otherresearchers (Yu et al. 2005), and the unsteady nature in centrifugal fans could be one of the rea-sons. Eventually, the convergence criteria were still set at 10–5, but the iterations were intention-ally stopped if periodical phenomenon occurred. The actual achieved convergence levels(residuals of continuity) are listed in Table 2.

The higher convergence levels imply that the result may be slightly away from the exact oneand may lead to imprecise simulation results. It should be noted that the convergence level ishigher around free delivery and shutoff conditions. Fortunately, the two extreme conditions arenot usually utilized in engineering applications. Comparing Model A to Model D in Table 2, itcan be found that the convergence level of the smaller blower (Model D) is higher. This trendconfirms the simulation results presented in the Results and Discussion section of this paper.

Table 2. Continuity Convergence Levels of Blowers Discussed in This Study

ModelFlow Rate

Low High

A 1.45×10-3 3.52×10-5 1.75×10-3 1.25×10-3 1.3×10-5 1.07×10-5 9.98×10-6 7.21×10-6 6.26×10-4

B 4.44×10-3 6.56×10-4 3.75×10-3 5.56×10-5 3.62×10-5 2.62×10-5 1.88×10-4 6.03×10-4 8.17×10-4

C 1.94×10-3 3.44×10-4 1.50×10-3 8.27×10-4 2.0×10-5 1.97×10-5 9.12×10-6 7.72×10-6 2.16×10-3

D 1.23×10-3 2.11×10-4 9.55×10-4 2.5×10-3 3.84×10-5 1.52×10-5 2.0×10-4 5.49×10-4 1.49×10-3

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The shaft power was calculated using Equation 2. FLUENT can compute and report momentsabout a specified center for selected wall zones. The total moment vector about a specified cen-ter is computed by summing the cross products of the pressure and viscous force vectors foreach face with the corresponding moment vector, which is the vector from the specified momentcenter to the force origin. Eventually, the efficiency can be calculated using Equation 3.

While the acoustic performance of the blower is important as well, its corresponding simula-tion is tougher and more time consuming. The CFD simulation process has to begin with asteady flow analysis, which includes all tasks described in this section. Thereafter, an unsteadycalculation is then performed using a sliding mesh. During the unsteady calculation, oscillatingvalues of pressure and velocity at several monitoring points located behind the rotating impellerwheel can be acquired. The periodic time histories of the pressure and the velocity values can beused to indicate when the unsteady flow calculation is fully developed. Only after this stage hasbeen reached is an unsteady acoustic analysis performed. For each case, the time needed to per-form an unsteady acoustic analysis can be weeks using a state-of-the-art system. Therefore, theacoustic analysis has not yet been performed in this research at this point.

EXPERIMENTAL VALIDATION

In this study, four blowers were tested in the Ventilation Systems Laboratory at the IndustrialTechnology Research Institute, Hsin-Chu, Taiwan. The laboratory possesses the facility for fanor blower performance tests in accordance with the requirements of ANSI/AMCA Standard210-07/ANSI/ASHRAE Standard 51-07, Laboratory Methods of Testing Fans for CertifiedAerodynamic Performance Rating (AMCA/ASHRAE 2007). The apparatus complied withAMCA 120/ASHRAE 51 (Figure 5). The wind tunnel is used to determine the aerodynamic per-formance of a fan or blower. The main components include the main structure (rectangle orround section is most seen), auxiliary supply system, grid, settling means, and multiple nozzlesto vary the airflow rate. The apparatus performs one of the most common procedures for devel-oping the characteristics of a blower tested from shutoff conditions to nearly free delivery condi-tions, while various flow restrictions are placed on the opening of the inlet duct to simulate

Figure 5. Schematic from AMCA 210/ASHRAE 51 (AMCA/ASHRAE 2007).

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VOLUME 15, NUMBER 3, MAY 2009 469

various conditions on the blower. In some cases, measurements are done by restrictions placedon the outlet duct. For those cases, the static pressure at the inlet is lower than the atmosphericpressure. The performance curves are obtained from sufficient points defined by the correspond-ing flow rate and static pressure rise. The static pressure rise, flow rate, and shaft power of theblower are obtained by measurement. The total pressure rise is obtained by the static pressureplus the averaged dynamic pressure head.

In this study, the uncertainty in the flow rate and the pressure measurements is ±2.5%. More-over, the fan input power obtained is within ±5%. Outlet velocity uniformity results obtainedare not different by more than ±7.5%. Velocity profile results obtained are not different bymore than ±7.5%. The rotational speed variation during the test is controlled within ±1%.Twenty-four measurements were made to derive the velocity profile and the correspondingflow rate.

When performing the blower tests, long ducts that are at least ten times the tube diameter areinstalled at the suction and discharge sides of the testing blower. As described previously, theinstallation of long inlet and outlet ducts was considered in our simulation.

RESULTS AND DISCUSSIONFor each model discussed in this study, the simulation and measured results are shown in two

plots, where the x-axes are both the input flow rate and the y-axes are static pressure and effi-ciency. Error bars for measurement data represent the measurement uncertainty acquired fromthe test facility. Error bars for simulation data are from additional simulations with maximumallowable rotational speeds when the measurement uncertainty is considered. However, the errorbars in Figure 10 are not from rotational speed variation since the results of two rotationalspeeds are shown; those error bars are from additional simulations with maximum allowablegeometry variation, which is ±2% enlargement or shrinkage on all parts.

From the manufacturer’s point of view, the four models belong to the same family (with thesame blade angle and blade number) and are mainly different in size. The blower size decreasesfrom Model A to D. For Model C, two rotational speeds were simulated to check the effective-ness of the simulation at different rotational speeds. For the other three models, only one rota-tional speed was simulated. By observing the results from all four models, the effects of blowersize on simulation effectiveness can be found. By comparing the Model C results from two rota-tional speeds, the effects of blower rotational speed on simulation effectiveness can be found.

Including simulation and measurement data, the performance curves of the four tested blow-ers are shown in Figures 6 through 9. It can be found that the simulation data agree well with themeasured results. The R-squared values were calculated and are listed in Table 3. R-squaredmeasures how successful the simulation is in explaining the variation of the measured data. Forall four models, the R-squared values of static pressure are close to 1, indicating that a greaterproportion of variance is accounted for by the simulation. On the other hand, the efficiencyresults are not as good as the static pressure ones; potential reasons for the imprecise efficiencysimulation will be discussed later. Furthermore, the root mean square error (RMSE) valuesbetween simulation and measurement (also listed in Table 3) for each model are calculated toexamine the closeness of the two curves. RMSE results imply that the simulation scheme pro-duces more precise results for larger blowers. Comparing the two rotational speeds of Model C(shown in Figure 10), it can be found that the simulation results deviate more at higher rotationalspeed. From the error bars in Figure 10, it can be found that the effects of geometry variation aregreater when operating conditions are closer to the free delivery condition.

Overall, the results indicate that the simulation scheme predicts the blower performancepretty well. The simulated static pressures are within 4.8% of the measured data. The efficiencycurves are relatively deviated and are within 15.1% of the measured data. Since the efficiency

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Figure 6a. Measured and simulated performance and efficiency curves of Model A oper-ating at 882% ± 1% rpm (SI units).

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Figure 6b. Measured and simulated performance and efficiency curves of Model A oper-ating at 882% ± 1% rpm (I-P units).

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Figure 7a. Measured and simulated performance and efficiency curves of Model B oper-ating at 980% ± 1% rpm (SI units).

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Figure 7b. Measured and simulated performance and efficiency curves of Model B oper-ating at 980% ± 1% rpm (I-P units).

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Figure 8a. Measured and simulated performance and efficiency curves of Model C oper-ating at 1280% ± 1% rpm (SI units).

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Figure 8b. Measured and simulated performance and efficiency curves of Model C oper-ating at 1280% ± 1% rpm (I-P units).

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Figure 9a. Measured and simulated performance and efficiency curves of Model D oper-ating at 1280% ± 1% rpm (SI units).

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Figure 9b. Measured and simulated performance and efficiency curves of Model D oper-ating at 1280% ± 1% rpm (I-P units).

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calculation is based on Equation 3, it is believed that the imprecise torque calculation may be themain cause of the error. The moment calculation consists of pressure and viscous parts, and theviscous part can be questionable. The viscous model may perform imprecise viscous calculationand lead to the moment calculation deviation. Since the simulation is based on a rotating fluidblock, the weight of the impeller wheel is not included to perform the moment calculation. Thismay also contribute the imprecise calculation.

It is also concluded that the current simulation scheme does a better job for blowers with alarger impeller wheel. For the same blower, the simulation is more precise for lower rotationalspeed. Based on the comparative results from the four models, it is believed the simulationscheme, including model construction in CAD, mesh generation, numerical simulation, andpost-processing, is successful. The process is able to predict the performance for future modelswithout requiring significant amounts of time and expense on prototypes and field tests. Afterthe simulation scheme was shown to be reliable, the process was utilized as a tool to discuss theeffects of some blower design parameters.

Effects of Blade AngleThe effects of blade angle can be estimated quantitatively from the theoretical equations.

From Equation 8, it can be found that the added head is a function of β2. When the blade angleincreases, then β2 increases. From 40° to 50°, cotangent is a decreasing function. Consequently,the increase of β2 will lead to the decrease of cot(β2) and the increase of added head. Thisimplies that, for the same flow rate, the added head increases when β2 increases.

In this simulation, we took 49.39° and 43.39° to perform the simulation and compared resultswith the original design of 46.49°. The schematic of impeller wheels with different blade anglesis shown in Figure 11. Comparative results are listed in Sets A and B of Table 4. It was foundthat a 49.39° blade angle exhibited much higher static pressure rise and slight efficiencydecrease. We decided the 49.39° was a favored blade angle, especially for applications where ahigh static pressure rise is needed.

Effects of Blade NumberThe number of blades directly affects the required material and manufacturing costs. Within

close performance, it is preferable to have as few blades as possible. Since a blade number of8 to 12 is usually recommended in the literature, blade numbers of 8, 10, and 14 were simulatedto compare with the blade number of 12. The schematic of impeller wheels with different bladenumbers is shown in Figure 12. From Sets C, D, and E in Table 4, it can be found that the bladenumber of 10 exhibits a slight decrease in static pressure and flow rate. From a manufacturingcost point of view, decreasing the number of blades from 12 to 10 is a favored change.

Table 3. R-Squared and RMSE between Measured and Simulated Static Pressure and Efficiency

Model/rpmStatic Pressure Efficiency

R-Squared RMSE, Pa (psi) R-Squared RMSE, %

Model A/882 1.11 41.74 (6.054×10–3) 0.85 5.73

Model B/980 1.17 48.31 (7.007×10–3) 0.91 6.70

Model C/1280 0.92 59.69 (8.657×10–3) 0.65 8.46

Model C/1470 0.95 74.42 (1.079×10–2) 0.64 9.17

Model D/1280 0.97 47.39 (6.873×10–3) 0.73 6.72

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Figure 10a. Measured and simulated performance and efficiency curves of Model C oper-ating at 1280 and 1470 rpm (SI units).

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Figure 10b. Measured and simulated performance and efficiency curves of Model Coperating at 1280 and 1470 rpm (I-P units).

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Table 4. Parameter Changes and the Corresponding Effects on the Blower Performance

Set A B C D E F G

Parameter change

Blade angle = 49.39°

Blade angle = 43.39°

Blade number

= 14

Bladenumber

= 10

Blade number

= 8

Tongue length

Scroll contour

by Bleier

Staticpressure* +20.39% –14.31% –0.69% –2.98% –11.67% +0.96% +4.19%

Efficiency* +0.75% –2.46% –1.13% –1.35% –3.96% +0.28% +2.02%

Peak efficiency

–2.18% –0.03% +0.26% –1.00% –3.56% –0.34% +0.84%

A favored parameter change?

Y N N Y N Y Y

*Flow rate at inlet = 357.4 m3/min (12620 ft3/min), the flow rate where approximately 50% of the maximum static pres-sure rise occurs.

Figure 11. Schematic of impeller wheels with different blade angles.

Figure 12. Schematic of impeller wheels with different blade numbers.

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Effects of Tongue LengthThe blower tongue is a short wall spirally extended from the scroll to the outer periphery of

the rotor. Intuitively, the tongue is installed to avoid back flow from the outlet region. Research-ers have shown that tongue form affects the blower performance (Katsumi and Tetsuo 1999). Itwould also be interesting to estimate the effects on the overall performance when we adjust thelength of the tongue. In this study, a half-long tongue was set to compare with the originalfull-length tongue. The schematic of scrolls with different tongue lengths is shown in Figure 13.Results from the short tongue length are listed in Set F of Table 4.

The results show that cutting the tongue length to one half slightly decreases the maximumefficiency but increases both efficiency and static pressure with a flow rate equal to357.4 m3/min (12620 ft3/min). Consequently, a half-long tongue is considered a favored change.

Effects of Scroll ContourIn fan/blower design handbooks, there are several recommended scroll contours and various

methods presented to obtain those contours. In this study, we followed the contour described inthe literature (Bleier 1998) and redesigned the scroll contour for Model A. The design criteriafollow.

• The scroll shape is approximated by three circular sections whose radii are 71.2%, 83.7%, and96.2% of the impeller wheel diameter.

• The centers of the three sections are located off the center lines by intervals of 6.25% of thewheel diameter.

• The height of the outlet is 112% the impeller wheel diameter.• The one-piece cutoff continues the curvature of the scroll and protrudes into the housing

outlet by 20% to 30% of the outlet height. The cutoff clearance is 5% to 10% of the wheeldiameter.

In Figure 14, the new contour is shown to the right of the original one. A schematic for Ble-ier’s (1998) parameters to construct the contour is also shown. Comparing the original and newscroll contours, the major difference is the length of the outlet and the design of the tongue.

The simulated results for the new contour are listed in Set G of Table 4. It is found that thenew contour increases static pressure and efficiency with a flow rate equal to 357.4 m3/min(12620 ft3/min) as well as peak efficiency. It can be concluded that a contour following Bleier’s

Figure 13. Schematic of scroll with different tongue lengths (left: original; right: one-halfof original).

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Figure 14. Scroll contours (top left: original; top-right: modified based on Bleier’s (1998)recommendation—dashed enclosures highlight the major differences; bottom: schematicof Bleier’s parameters to construct the contour).

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(1998) recommendation indeed improves the blower performance and can be considered afavored parameter change.

OPTIMIZED DESIGNThe effects of blade angle, blade number, tongue length, and scroll contour have been dis-

cussed in the previous section are organized in Table 4. It should be noticed that the recommen-dations in Table 4 are based on cost/performance and the balance between higher static pressurerise, higher flow rate, and lower manufacturing cost. Based on the conclusions recorded inTable 4, the virtual Model A+ was modified from Model A with all favored parameter changes:A, D, and G.

The schematic of the impeller wheel and the scroll for virtual Model A+ is shown inFigure 15. The virtual Model A+ was first constructed in CAD and then imported into GAMBITand FLUENT. Simulations were performed to produce performance data. Comparing simulatedresults between Models A and A+, the performance and efficiency curves are shown inFigure 16. It can be found that the performance curve for the optimized model movesupward-right, meaning higher static pressure and volume flow rate. The peak efficiency for theoptimized model decreases about 5%. However, the efficiency increases significantly in the highflow rate region. Taking an average from all operating points, the optimized design exhibits a7.9% improvement in static pressure and a 1.5% improvement in efficiency. The results showthat the optimization is successful. The conclusive favored parameter changes are a valuable ref-erence for future blower designs.

CONCLUSIONIn this study, backward-curved airfoil centrifugal blowers were numerically simulated and

analyzed. The results from numerical simulations and measurements were compared to verifythe validity of numerical simulation.

The numerical simulations of centrifugal blowers are shown to be effective. The deviations ofthe performance curves and the efficiency curves are within 4.8% and 15.1%, respectively. Theeffects of blade angle, blade number, tongue length, and scroll contour were numerically stud-ied. Some favored parameter changes were determined and utilized to redesign one of the

Figure 15. Schematic of the blower with the optimized parameters (virtual Model A+).

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VOLUME 15, NUMBER 3, MAY 2009 485

Figure 16a. Performance comparison between Model A and virtual Model A+ (SI units).

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Figure 16b. Performance comparison between Model A and virtual Model A+ (I-P units).

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VOLUME 15, NUMBER 3, MAY 2009 487

blowers. The optimized model indeed exhibits a better value of cost/performance. This furthershows that the presented simulation scheme is successful and that the favored parameter changesare a good reference for future blower designs.

ACKNOWLEDGMENTThe authors gratefully acknowledge the support from National Science Council (NSC) of Tai-

wan (Grant number NSC 94-2622-E-027-045-CC3).

NOMENCLATURE

bhp = brake horsepower, W (Btu/h)g = acceleration of gravity, m/s2 (ft/s2)H = net head, m (ft)

= mass flow rate, kg/s (lb/s)Q = volume flow rate, m3/s (ft3/m)r = radius, m (ft)

T = torque, N⋅m (ft⋅lbf)

U = tangential speed, m/s (ft/s)

V = velocity, m/s (ft/s)

w = impeller wheel width, m(ft)

W = work, J (Btu)

Greek Symbols

β = blade angle, °η = efficiency, %

ρ = density, kg/m3 (lb/ft3)ω = rotational speed, rad/s

Subscripts

1 = inner periphery of impeller wheel2 = outer periphery of impeller wheel

t = tangential componentn = normal component

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